Seeding experiments achieved with gas amplifiers demonstrated high quality X ray beams. Since amplifiers based on solid targets are denser than those generated from gas, higher energy and shorter pulse durations were expected. However, experiments demonstrated lower energy around 90 nJ and slightly shorter pulse duration down to 1 ps. We concentrated this thesis on the understanding of the mismatch between expected and measured energies for solid targets with the goal to find a way for producing seeded plasma-based soft x-ray laser emitting tens of microjoules per pulse as required by many applications. This work has been done with the code ARWEN. This code had already been used in this field but it has been improved in the frame of this thesis, adding new computational capabilities. The work presented in this thesis is: - Theoretical study of coherent X-ray sources, emphasizing the plasma-based sources. The state of the art and the physics of these amplifiers are described more thoroughly. - Description of the ARWEN code, the fundamental tool of this work, and the improvements introduced in it (ray tracing, parallelization of thermal conduction subroutines, standard HDF output, etc...). In addition to this, the codes used for prostprocessing the data are also described. - Optimization of plasma amplifiers by means of numerical models. These studies start from previous works, continuing the work and explaining the effects that lead to the differences between the predicted energy and the energy experimentally observed. Some ways to avoid these effects are proposed. An study of the amplification of the injected seed in these plasmas is also presented, concluding that pre-amplifier stages are essential. Thus, nowadays a code with new simulation capabilities (ARWEN)is available and it can be applied to several fields (not only plasma-based soft X-ray lasers). It has been used to study plasma-based amplifiers, gaining an insight into the physics of these systems, explaining the differences between experimental results and theoretical predictions. In addition to this, it has been proposed a new scheme to optimize these amplifiers.